\chapter{Experimental Setup}

\begin{figure}
\begin{center}
	\includegraphics{setup_diagram.pdf}
	\caption[Experimental setup for counterpropagating beams]{\label{fig:setup} Experimental setup for transverse optical pattern generation. The output of a frequency-stabilized cw Ti:Sapphire laser serves as the source. A polarizing beamsplitter (PBS1) separates the forward (cw) and backward (ccw) beams within the triangular ring cavity. The backward beam is brought into horizontal polarization by a half-wave plate ($\lambda$/2). The forward and backward beams counterpropagate through a warm $^{87}$Rb vapor contained in a 5-cm glass cell. A polarizing beam-splitter (PBS2) reflects instability-generated light in the vertical polarization which is observed by a CCD camera and avalanche photodiode (APD).}
\end{center}
\end{figure}

A diagram of our experimental setup is shown in Fig.~\ref{fig:setup}. Two beams of light from a common laser source counterpropagate through warm rubidium vapor contained in a glass cell. The light source is a frequency-stabilized continuous-wave Ti:Sapphire laser, the output of which is spatially filtered using a single-mode optical fiber with an angled entrance face and a flat-polished exit face. The beam is then collimated to a spot size (1/e field radius) of $w$ = 340 $\mu$m with the beam waist located at the center of the vapor cell. The power ratio between the pump beams is controlled by a half-wave plate at the input of the first polarizing beam splitter (PBS1). We denote the beam passing through PBS1 as the forward beam and the reflected beam as the backward beam. A second half-wave plate in the backward beam path rotates the polarization such that the pump beams are linearly polarized with parallel polarizations.

The atomic medium is isotopically-enriched rubidium vapor ($>$ 90\% $^{87}$Rb), which is contained in a 5-cm-long glass cell heated to 67 $^{\circ}$C (corresponding to an atomic number density of $\sim 2 \times 10^{11}$ atoms/cm$^3$). The cell is tilted with respect to the incident laser beams to prevent possible oscillation between the uncoated windows. The cell has no paraffin coating on the interior walls that would prevent depolarization of the ground-state coherence, nor does it contain a buffer gas that would slow diffusion of atoms out of the pump laser beams. The Doppler-broadened linewidth of the transition at this temperature is $\sim$550 MHz. To prevent the occurrence of magnetically-induced instabilities and reduce Faraday rotation, we use a Helmholtz coil to cancel the ambient magnetic field component along the direction of the counterpropagating laser beams.

A polarizing beam splitter (PBS2) placed in the beam path separates light polarized orthogonally to the pump beam. This light, henceforth referred to as \emph{output} light, is subsequently split with a 50/50 beamsplitter and then observed simultaneously using any two of the following: a CCD-camera (Marshall V-1050A), an avalanche photodiode (Hamamatsu C5460), or a photomultiplier tube (Hamamatsu H6780-20) as shown in Fig.~\ref{fig:setup}.